Displaying similar documents to “Mating quadratic maps with Kleinian groups via quasiconformal surgery.”

Loewner chains and quasiconformal extension of holomorphic mappings

Hidetaka Hamada, Gabriela Kohr (2003)

Annales Polonici Mathematici

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Let f(z,t) be a Loewner chain on the Euclidean unit ball B in ℂⁿ. Assume that f(z) = f(z,0) is quasiconformal. We give a sufficient condition for f to extend to a quasiconformal homeomorphism of ℝ 2 n onto itself.

Composition operators on W 1 X are necessarily induced by quasiconformal mappings

Luděk Kleprlík (2014)

Open Mathematics

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Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.